Chapter 24 - Valn of asset classes & portfolios

Hi Fischer

I wonder if your example would work better with longer-term liabilities as it is then that I think you would observe more of a difference between a market-related discount rate and a long-term expected return.

Suppose that, 3 years' ago, a life insurer took on a one-off 20-year liability of £100,000, which it matched from outset with a 20-year zero-coupon bond. When the bond is purchased, its long-term expected return (or GRY) is 5%.

Using the discounted cashflow method (where the same discount rate is used for both A and L).

Value of assets = £100,000 / (1+i)^17 at i = 5%
Value of liabilities = £100,000 / (1+i)^17 at i = 5%

Using the market value apporach.

Value of assets = market value
Value of liabilities = £100,000 / (1+i)^17 at i = market-related discount rate

The market-related discount rate would be determined by looking at the current GRY on a 17-year ZCB. This could well have shifted from the 5% yield at which the bond was purchased. The current yield could be 4%, in which case i = 4%.

Another example would be for liabilities backed with equities. A life company's long-term view for the expected return on equities might be 7%.

Using the discounted cashflow method, both assets and liabilities would be valued using a discount rate of 7%. On the asset side, dividends would be projected using a dividend growth rate of g and discounted at 7%. On the liabilities side, the cashflows would be projected and then discounted at 7%.

Using the market value approach, the assets would be valued at market value. The liability cashflows would be projected and then discounted at a market-related rate. This market-related rate could be determined as the current GRY on a government bond of a suitably matcing duration to the liabilities + an equity risk premium.

 

Hi Fischer

I wonder if your example would work better with longer-term liabilities as it is then that I think you would observe more of a difference between a market-related discount rate and a long-term expected return.

Suppose that, 3 years' ago, a life insurer took on a one-off 20-year liability of £100,000, which it matched from outset with a 20-year zero-coupon bond. The company's long-term expected return on bonds is 5%. This may be based on what the GRY on the bond was at purchase or some other analysis that the company has done.

Using the discounted cashflow method (where the same discount rate is used for both A and L):

Value of assets = £100,000 / (1+i)^17 at i = 5%
Value of liabilities = £100,000 / (1+i)^17 at i = 5%

Using the market value apporach:

Value of assets = market value
Value of liabilities = £100,000 / (1+i)^17 at i = market-related discount rate

The market-related discount rate would be determined by looking at the current GRY on a 17-year ZCB. The current GRY will reflect all sorts of things, including current market sentiment and could well be different from 5%. Let's say the current GRY on 17-year bonds is 4%, in which case i = 4%.

Another example would be for liabilities backed with equities. A life company's long-term view for the expected return on equities might be 7%.

Using the discounted cashflow method, both assets and liabilities would be valued using a discount rate of 7%. On the asset side, dividends would be projected using a dividend growth rate of g and discounted at 7%. On the liabilities side, the cashflows would be projected and then discounted at 7%.

Using the market value approach, the assets would be valued at market value. The liability cashflows would be projected and then discounted at a market-related rate. This market-related rate could be determined as the current GRY on a government bond of a suitably matcing duration to the liabilities + an equity risk premium.

Anna